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IOP Publishing, Journal of Physics A: Mathematical and General, 39(32), p. 6791-6820

DOI: 10.1088/0305-4470/32/39/307

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Spectral Statistics in Chaotic Systems with Two Identical Connected Cells

Journal article published in 1999 by Thomas Dittrich, Gert Koboldt, Bernhard Mehlig ORCID, Holger Schanz
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This paper is available in a repository.

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Abstract

Chaotic systems that decompose into two cells connected only by a narrow channel exhibit characteristic deviations of their quantum spectral statistics from the canonical random-matrix ensembles. The equilibration between the cells introduces an additional classical timescale that is also manifest in the spectral form factor. If the two cells are related by a spatial symmetry, the spectrum shows doublets, reflected in the form factor as a positive peak around the Heisenberg time. We combine a semiclassical analysis with an independent random-matrix approach to the doublet splittings to obtain the form factor on all time (energy) scales. Its only free parameter is the characteristic exchange time between the cells in units of the Heisenberg time.